中文摘要：

图像去噪是图像处理中最基本的问题,也是当前研究的热点。近年来,国内外学者对去除乘性噪声进行了大量的研究,在AA模型的基础上提出了许多去除合成孔径雷达图像中的伽马噪声的模型,它们都可以有效地去除图像中的噪声,但是共同的缺点是原图像的细节丢失并且计算速度慢。针对这些问题,引入了权重函数,在此基础上给出一种基于偏微分方程的去除图像乘性噪声的变分模型。然后使用交替迭代法,求出了该模型的数值解,并从理论上说明了该迭代序列的收敛性。数值实验结果表明,所提出的模型保持了较好的去噪效果,能够较好地抑制图像中的“阶梯效应”;与其他模型相比,该算法处理速度快,极大地缩短了运算时间。

英文摘要：

Image denoising is the most basic problem in image processing and also the current research focus. In recently years, there are a lot of researches on the multiplicative noise removal by domestic and foreign scholars. Based on AA model, many models for removal of Gamma noise in synthetic aperture radar image are proposed, which can remove the noise effectively, but the common disadvantage is loss of the original image＇ s detail and slow computing speed. Aiming at them,introducing weight funetion,a new variational model based on partial differential equation is proposed to remove the multiplicative noise. An alternating minimization algorithm is introduced to solve the problem for the model. What＇ s more, the convergence for the variational problem is illustrated in theroy. Experimental results show that the proposed model has a good denoising effect and restrains the ＂staircase effect＂. Compared with the other models, the algorithm is faster and greatly decreases the computational time.